Bearings from one point: change the true bearing of P and see the angle between two bearings and the area of the triangle they make
Two bearings from one point fix a triangle
A true bearing gives a direction as three digits measured clockwise from north. Take two bearings and two distances from the same point and you have a triangle you can solve: the angle between the bearings, then the sides and area with trigonometry. Here Q is fixed at 120°, 70 m from the observer. Swing the bearing of P (85 m away) and watch the angle between the bearings, and the area of the triangle, change.
Bearings from one point
BEARING 045°
Change the bearing of P (000° to 360°)
Area = ½ × 85 × 70 × sin 75° = 2874 m²
Bearing angle
000°090°180°270°360°
Current bearing
045°
Triangle area
2874 m²
True bearings are always written as three digits measured clockwise from north: 045° not 45°, 008° not 8°. This removes ambiguity in navigation. When solving multi-step bearing problems, sketch the triangle first and identify which sides and angles you know. The sine rule connects opposite pairs (side/angle), while the cosine rule handles situations where you know two sides and the included angle. Back bearings (the reverse direction) differ by exactly 180°, so a bearing of 045° has a back bearing of 225°.
Know This
True bearings are three-digit angles clockwise from north, elevation angles measure up from horizontal, and two bearings from one point give the angle between them, so the triangle they make can be solved, including its area, ½ab sin C.